What is the general solution for 4sin(t/2)-1=1 ?

The general solution for 4sin(t/2)-1=1 is t= pi/3+4pin,t=(5pi)/3+4pin

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4sin(t/2)-1=1

4 sin (\frac{t}{2}) - 1 = 1

t = \frac{π}{3} + 4 πn, t = \frac{5 π}{3} + 4 πn

Solution steps

4 sin (\frac{t}{2}) - 1 = 1

Move

1

to the right side

4 sin (\frac{t}{2}) = 2

Divide both sides by

4

sin (\frac{t}{2}) = \frac{1}{2}

General solutions for

sin (\frac{t}{2}) = \frac{1}{2}

\frac{t}{2} = \frac{π}{6} + 2 πn, \frac{t}{2} = \frac{5 π}{6} + 2 πn

Solve

\frac{t}{2} = \frac{π}{6} + 2 πn : t = \frac{π}{3} + 4 πn

Solve

\frac{t}{2} = \frac{5 π}{6} + 2 πn : t = \frac{5 π}{3} + 4 πn

t = \frac{π}{3} + 4 πn, t = \frac{5 π}{3} + 4 πn

2 cos^{2} (x) = sin (2 x)

tan (θ) + cot (θ) = 4 sin (2 θ)

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0

sin (x) = 0, 0 \leq x \leq 2 π

tan (x) sin (x) - 4 tan (x) = - 3 tan (x)

What is the general solution for 4sin(t/2)-1=1 ?
The general solution for 4sin(t/2)-1=1 is t= pi/3+4pin,t=(5pi)/3+4pin